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We show the homological Serre spectral sequence with coefficients in a field is a spectral sequence of coalgebras. We also identify the comultiplication on the $E^2$ page of the spectral sequence as being induced by the usual comultiplication in homology. At the end, we provide some example computations highlighting the use the co-Leibniz rule.
We construct using relatively basic techniques a spectral sequence for exact Lagrangians in cotangent bundles similar to the one constructed by Fukaya, Seidel, and Smith. That spectral sequence was used to prove that exact relative spin Lagrangians i
We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2-primary part of $pi_{51}$ is $mathbb{Z}/8oplusmathbb{Z}/8oplusmathbb{Z}/2$. This was the last unsolved 2-extension problem left by the
In previous work of the first author and Jibladze, the $E_3$-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the $E_3
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
We make a conjecture about all the relations in the $E_2$ page of the May spectral sequence and prove it in a subalgebra which covers a large range of dimensions. We conjecture that the $E_2$ page is nilpotent free and also prove it in this subalgebr